Modeling active electrolocation in weakly electric fish

TL;DR

This paper develops a mathematical model for electrolocation in weakly electric fish, introducing a non-iterative localization algorithm and methods to reconstruct target properties from multi-frequency data.

Contribution

It presents a new mathematical framework and algorithms for modeling electrolocation and reconstructing target properties in weakly electric fish.

Findings

The proposed multi-frequency location search algorithm is effective and stable.

Numerical experiments demonstrate the accuracy of the localization method.

Reconstruction of conductivity, permittivity, and size is feasible for specific target shapes.

Abstract

In this paper, we provide a mathematical model for the electrolocation in weakly electric fishes. We first investigate the forward complex conductivity problem and derive the approximate boundary conditions on the skin of the fish. Then we provide a dipole approximation for small targets away from the fish. Based on this approximation, we obtain a non-iterative location search algorithm using multi-frequency measurements. We present numerical experiments to illustrate the performance and the stability of the proposed multi-frequency location search algorithm. Finally, in the case of disk- and ellipse-shaped targets, we provide a method to reconstruct separately the conductivity, the permittivity, and the size of the targets from multi-frequency measurements.